عنوان

Philosophy of mathematics :

1405189916 (pbk. : alk. paper)

1405189924 (hardcover : alk. paper)

9781405189910 (pbk. : alk. paper)

9781405189927 (hardcover : alk. paper)

dltt

Philosophy of mathematics :

[Book]

an introduction /

David Bostock

Malden, MA :

Wiley-Blackwell,

2009

x, 332 p. :

ill. ;

24 cm

Includes bibliographical references (p. [310]-324) and index

1.Plato versus Aristotle -- A. Plato -- The Socratic background -- The theory of recollection -- Platonism in mathematics -- Retractions: the divided line in Republic VI (509d-511e) -- B. Aristotle -- The overall position -- Idealisations -- Complications -- Problems with infinity -- C. Prospects -- 2. From Aristotle to Kant -- Medieval times -- Descartes -- Locke, Berkeley, Hume -- A remark on conceptualism -- Kant: the problem -- Kant: the solution -- 3.Reactions to Kant -- Mill on geometry -- Mill versus Frege on arithmetic -- Analytic truths -- Concluding remarks -- 4.Mathematics and its Foundations -- Geometry -- Different kinds of number -- The calculus -- Return to Foundations -- Infinite numbers -- Foundations again -- 5.Logicism -- Frege -- Russell -- Borkowski/Bostock -- Set theory -- Logic -- Definition -- 6.Formalism -- Hilbert -- Gödel -- Pure formalism -- Structuralism -- Some comments -- 7.Intuitionism -- Brouwer -- Intuitionist logic -- The irrelevance of ontology -- The attack on classical logic -- 8.Predicativism -- Russell and the VCP -- Russell's ramified theory and the axiom of reducibility -- Predicative theories after Russell -- 9.Realism versus Nominalism -- A. Realism -- Gödel -- Neo-Fregeans -- Quine and Putnam -- B. Nominalism -- Reductive nominalism -- Fictionalism -- Concluding remarks

0

Mathematics-- Philosophy

Bostock, David

20091114113758.0

[Book]

Y